Which of the following numbers is a multiple of 11? ${55,64,65,81,113}$
Explanation: The multiples of $11$ are $11$ $22$ $33$ $44$ ..... In general, any number that leaves no remainder when divided by $11$ is considered a multiple of $11$ We can start by dividing each of our answer choices by $11$ $55 \div 11 = 5$ $64 \div 11 = 5\text{ R }9$ $65 \div 11 = 5\text{ R }10$ $81 \div 11 = 7\text{ R }4$ $113 \div 11 = 10\text{ R }3$ The only answer choice that leaves no remainder after the division is $55$ $ 5$ $11$ $55$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $11$ are contained within the prime factors of $55$ $55 = 5\times11 11 = 11$ Therefore the only multiple of $11$ out of our choices is $55$. We can say that $55$ is divisible by $11$.